|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Bjoerck A., Dahlquist G. — Numerical mathematics and scientific computation |
|
|
|
| Предметный указатель |
A-norm 333
A-orthogonal vectors 336
Adjoint matrix 190
Aitken extrapolation 237
Algorithm,  29
Algorithm, back-substitution 6
Algorithm, back-substitution, banded 25
Algorithm, band LU 24
Algorithm, band-Cholesky 36
Algorithm, block Cholesky 48
Algorithm, block LU factorization 47
Algorithm, block-Cholesky factorization 48
Algorithm, CG 340
Algorithm, CGLS 351
Algorithm, CGNE 351
Algorithm, CGNR 365
Algorithm, Cholesky factorization 34
Algorithm, classical Gram — Schmidt 121
Algorithm, compact LU 19
Algorithm, Euler — Newton method 399
Algorithm, forward-substitution, banded 25
Algorithm, Gaussian elimination 7
Algorithm, Givens rotations 132 247
Algorithm, Householder QR 136
Algorithm, Householder reflection 131
Algorithm, incomplete Cholesky 372
Algorithm, incomplete LU 369
Algorithm, IRLS 183
Algorithm, Lanczos 285 359
Algorithm, MGS, least squares by 126
Algorithm, MGS, minimum norm solution by 127
Algorithm, modified Gram — Schmidt 123
Algorithm, orthogonal iteration 281
Algorithm, preconditioned CG 363
Algorithm, preconditioned CGNE 365
Algorithm, Rayleigh — Ritz procedure 279
Algorithm, recursive Cholesky factorization 51
Algorithm, svd 230 234
Algorithm, The Arnoldi process 288
Algorithm, tridiagonal spectrum slicing 254
Algorithm, Vandermonde system 85
Algorithm, Vandermonde system, dual 84
Analytic function of matrix 207
Armijo — Goldstein criterion 396
Arnoldi's method 288—289 354—358
Arnoldi's process 355
Arrowhead matrix 253
Augmented linear system 96
Augmented system 140—141
B-splines, cubic 142
Back-substitution 5
Back-substitution, banded 25
Banach space 387
Banded matrix of standard form 141
Banded systems 23—36
Bandwidth of LU factors 23
Bandwidth, lower 23
Bandwidth, row 101
Bandwidth, upper 23
Bauer — Fike's theorem 217
BCG see "Bi-conjugate gradient"
BFGS update 406
Bi-conjugate gradient method 360
Bidiagonal decomposition, Lanczos process 287
Bidiagonal form, reduction to 153—155
Bidiagonal matrix 23
Bilinear 442
Bordered matrix 54
Broyden's method 393
Canonical form, Kronecker 291
Canonical form, Schur 199—202
Cauchy matrix 87
Cayley — Hamilton theorem 204
CG see also "Conjugate gradient"
CG method, preconditioned 363—364
cgs 361 see
Characteristic equation 191
Characteristic polynomial 191
Chebyshev polynomials 328
Chebyshev semi-iterative method 330
Cholesky factorization 33—37 100
Cholesky factorization, backward error 74
Cholesky factorization, block incomplete 373
Cholesky factorization, incomplete 371
Cholesky factorization, sparse 62
Cholesky factorization, symbolic 62
Column scaling 117
Column scaling, optimal 105
Condition estimation 71—72 157—158
Condition estimation, Hager's 72
Condition number of matrix 65
Condition number, general matrix 115
Conjugate gradient method 338—344
Conjugate gradient method, preconditioned 364—366
Conjugate gradient method, rate of convergence 342
Conjugate residual method 341 345
Consistently ordered 320
Constrained problem, quadratic inequality 172—175
Continuation method 398—399
Contraction 386
Contraction mapping theorem 386
Convergence, acceleration of 327—331
Convergence, asymptotic rate 311
Convergence, average rate 311
Convergence, conditions for 309
Convergent matrix 309
Convex set 427
Cost vector 427
Covariance matrix 92—94 102
Covariance matrix, estimate 101
Covariance matrix, method 161
Craig's method 351
Cramer's rule 2
Crout's algorithm 19
CS decomposition 295—296
Decomposition, block diagonal 202
Decomposition, CS 295—296
Decomposition, GSVD 296
Decomposition, SVD 108
Defect matrix 374
Deflation 238—239
Deflation of matrix 195 239
Degeneracy 434—436
Departure from normality 202
Derivative, directional 444
Derivative, Frechet 444
Derivative, Gateaux 444
Derivative, higher, vector-valued 444
Derivative, partial 444
Descent direction 395 403
Diagonal scaling, optimal 368
Differentials, elementary 447
Direct elimination, method of 170
Direct methods, fast 374—376
Directional derivative 444
Distance to singular matrices 67
Divide and conquer, tridiagonal eigenproblem 252—253
Dominant, invariant subspace 244
Doolittle's algorithm 19
Double pendulum 401
Downdating, Cholesky factorization 168
Downdating, Gram — Schmidt decomposition 167—168
Downdating, QR decomposition 166—167
Downdating, Saunders algorithm 170
Eigenvalue by spectrum slicing 254—256
Eigenvalue of Kronecker product 197
Eigenvalue of Kronecker sum 197
Eigenvalue of matrix 191
Eigenvalue problem, large 278—289
Eigenvalue, algebraic multiplicity 195
| Eigenvalue, defective 196
Eigenvalue, dominant 237
Eigenvalue, error bound 223—226
Eigenvalue, geometric multiplicity 195
Eigenvalue, Jacobi's method 229—232
Eigenvalue, perturbation 217—226
Eigenvalue, power method 236—245
Eigenvalue, subspace iteration 243—245
Eigenvector of matrix 191
Eigenvector, perturbation 217—226
Element growth 10 27 73
Element growth, Bunch — Kaufman pivoting 39
Element growth, complete pivoting 74
Element growth, partial pivoting 74
Elementary differentials 447 450
Elementary reflector 130
Elementary rotations, unitary 236
Elliptic equation 344
Envelope of LU factors 56
Envelope of matrix 56
Error bounds, a posteriori 70
Error bounds, backward 69
Error, componentwise estimate 158
Errors-in-variable model 178
Euler expansion 377
Exchange matrix 22
Expansion, Euler 377
Expansion, Neumann 377
Exponential fitting 408
Exponential of matrix 206
Fast Fourier Transform 375
Feasible point 384
Feasible point, basic 430
Feasible point, degenerate 430
Feasible region 384
Field of values 224
Fill-in 55
Filter factor 146
Fischer's theorem 111 221
Fixed Point Iteration 385—388
FLOP 7
Flop count, 30
Flop count, banded back-substitution 25
Flop count, banded LU 25
Flop count, Cholesky factorization 100
Flop count, condition estimation 72
Flop count, Gauss — Jordan elimination 18
Flop count, Gaussian elimination 8
Flop count, Gram — Schmidt 123
Flop count, Hessenberg system 25
Flop count, Householder QR 144
Flop count, inverse matrix 21
Flop count, normal equations 100
Flop count, QR algorithm for SVD 274
Flop count, QR factorization 137 158
Flop count, QR factorization, banded 141
Flop count, QR step 262
Flop count, reduction to bidiagonal form 154
Flop count, reduction to Hessenberg form 249 250
Flop count, triangular system 8
Flop count, tridiagonal system 26
Forward-substitution, banded 25
Frechet derivative 443
Functional equation 383
Functions, matrix-valued 206—212
Fundamental subspaces 114
Gap of spectrum 279
Gateaux derivative 444
Gauss — Jordan elimination 18
Gauss — Markoff 's theorem 93
Gauss — Newton method 409—413
Gauss — Newton method, rate of convergence 413
Gauss — Seidel's method 304 335
Gauss — Seidel's method, nonlinear 385
Gaussian elimination 3—20
Gaussian elimination, backward error 73
Gaussian elimination, block algorithms 46—53
Gaussian elimination, compact schemes 18—20
Gaussian elimination, matrix representation of 15
Gaussian elimination, rounding error analysis 73—76
Gaussian elimination, scaling invariance 77
ge see "Gaussian elimination"
Generalized eigenvalue problem 290—294
Generalized SVD 296—297
Geometric fitting 420
Gershgorin disks 215
Gershgorin's theorem 215 216
Givens rotation 131
Givens rotation, unitary 247
GKBD see "Golub — Kahan bidiagonalization"
Global convergence 395—397
gmres 354—358
GMRES, preconditioned 366
GMRES, restarted 358
Golub — Kahan bidiagonalization 287—288 352
Golub — Kahan bidiagonalization in finite precision 288
Grade of vector 196
Graded matrix 251
Gradient vector 387 402
Gram — Schmidt decomposition, downdating of 167—168
Gram — Schmidt decomposition, modifying 167—168
Gram — Schmidt, classical 121
Gram — Schmidt, modified 123
Gram — Schmidt, orthogonalization 121—129
Graph, connected 193
Graph, directed 193
Graph, ordered 59
Graph, undirected 59
Growth ratio 10 73 250
Hankel matrix 86
Hermitian matrix 190
Hessenberg form, reduction to 248—250
Hessenberg matrix 23
Hessenberg matrix, unreduced 198 263
Hessian matrix 402 445
Hestenes method 233—234
Hilbert matrix 87
Homotopy 398
Hotelling 239
Householder reflection, unitary 247
Householder reflector 130
Hyperbolic rotations 133
ill-posed problems 172—175
Implicit function 443
Incomplete factorization 369—374
Incomplete factorization, block 372—374
Incomplete factorization, Cholesky 371
Incomplete factorization, LU 369
Incremental loading 399
Inertia of matrix 223
Initial basis 437
Inner iteration 373
Instability, irrelevant 249
Invariant subspace 193
Inverse function 443
Inverse iteration 239—242
Inverse iteration, shift 240
Inverse of band matrix 26
Inverse, left 121
Inverse, product form of 18
IRLS see "Iteratively reweighted least squares"
Iteration matrix 308
Iteration matrix, Gauss — Seidel 309
Iteration matrix, Jacobi 309
Iteration matrix, SOR 319
Iteration matrix, SSOR 324
Iterative method, block 325—326
Iterative method, classical 348
Iterative method, convergent 309
Iterative method, error reducing 350
|
|
|
| Реклама |
|
|
|
|
|
|
|
|
О проекте